

where \(v_0=v(R_{\mathrm {p}})\) , \(\rho _0=\rho (R_{\mathrm {p}})\) , and
\(a\)  and \({\sigma }\)  are respectively the radiation and Stefan–Boltzmann constants.
[1]} found that the entire mechanical energy goes into radiation. Thus the radiation flux from accretion is \({F_{\textnormal {acc}}} = 0.5 \rho _0 v_0^3\) , leading to Equation (REF ). When \(\dot{M} \approx 0\) , the choice of \({T_{\textnormal {int}}}\approx 1100\)  K sets a minimum of \(T_0\approx 800\)  K (since \(4{\sigma }=ac\) ; \({T_{\textnormal {int}}}\)  is an effective temperature but \(T_0\)  a material temperature).
